construct a quadratic equation

Question

construct a quadratic equation for which -3 and 5 are solutions. 

Answer 1

Just put the two given roots in linear factors:

 

(x - r1)(x - r2) = 0

 

[x - (-3)](x-5) = 0

 

Finally,

 

f(x) = (x+3)(x-5)

 

By inspection, f(x) = 0 has roots -3 and 5.